segmentation of deformable objects in image guided surgery using ...

SEGMENTATION OF DEFORMABLE OBJECTS IN IMAGE GUIDED SURGERY USING RADIAL ACTIVE RAY AND ACTIVE CONTOUR MODEL ALKESH BHOJABHAI MUNGRA1, GOPALKRISHNA M. T.2 1

ISE Department, 2Associate Prof. of ISE Department, Dayananda Sagar College of Engineering, Bangalore,India

Abstract- In this Paper, Segmentation of deformable objects using our proposed method is discussed. Segmentation of deformable object is very much useful specially in case of medical image processing applications. This paper represent methods based on Radial Active Ray method, Active contour model with Gradient vector flow field. Segmentation of deformable objects is very difficult for medical images due to poor resolution and weak contrast, but still these techniques gives correct result and the result of these techniques is useful in further processing like deformable object tracking in Laproscopic surgery. Index Terms- Deformable objects, Active contours, Radial active ray, Gradient vector flow.

boundary regios. For example pressure forces, which can push an active contour into boundary concavities, but it requires the priori knowledge of whether to shrink or expand the contour.

I. INTRODUCTION Segmentation is the process of separating objects in an image. The underlying objective of medical image segmentation is to partition it into different anatomical structures, thereby separating the components of interest, such as blood vessels and liver tumors, from their background. The Objects whose shape is not in proper geometry like rectangle, circle, square and Objects which changes its shape in each frame of video are called Deformable objects. Computerized medical image segmentation is a challenging problem, due to weak image edges. Moreover the task is often made more difficult by the presence of noise and artifacts, due to instrumental limitations, refconstruction algorithms and patient movement. There is yet no universal algorithm for medical image segmentation. An algorithm’s advantages and drawbacks often vary according to the problem under investigation.

II. BACKGROUND A. Active contour model with Gradient Vector Flow(GVF) Active contour model, also called Snakes, is a framework. An active contour model (ACM) is a technique for contour extraction based on the principle of minimization of the energy defined on a closed curve comprising control points. It extracts object at a high contrast against a background and for distinguishing smooth forms. The primary condition for Snake is the initialization of the contour. This significantly influences the final result. In case of variations in a mass, it is not easy to recognize the size, form, and position of the target, and in such cases, even if it is not desirable, the initial contour must be set up manually.

To overcome these limitations many methods have been introduced. These methods requires approximate initialization of contour by manual intervention, so that then it will move towards the desired contour. In [2] fuzzy level set segmentation method is discussed which makes contour initialization by manual intervention then uses fuzzy clustering for the estimation of contour controlling parameters. In [7] Active contour model with gradient vector flow as external force is discussed that focus on the gradient vector of the image to move initial contour towards the desired contour. Traditional methods which are based on thresholding and region growing or merging can not give accurate result because of its limitation. Although many methods such as multiresolution methods, pressure forces, distance potential Forces, control points, and using solenoid external fields have been proposed, but they can not work for concave and convex

Snake is mathematically represented using the following equation. (1) where: energy function of the active contour from which an object is detected. the contour(curve). the internal energy of the active contour affecting the motion of the contour. the external constraint imposed by either users or high level processes. This is also called Snake termination condition minimum( ) then because when value of Snake stops further movement from that point.

International Conference on Intelligent Systems Technologies and Computer Applications, 15th September, 2013, Chandigarh, ISBN: 978-93-83060-13-9 16

Segmentation of Deformable Objects in Image Guided Surgery Using Radial Active Ray and Active Contour Model

1) Internal Energy Internal forces are called elasticity forces and it keeps Snake from bending too much. Internalenergy can be written as (2) where: calculatesthe energy The first derivative affecting the elasticity of the contour. is the parameter for elasticity. calculatesthe energy The second derivative affecting the curvature of the contour. is the parameter of the curvature.

is more noise ,then increase µ. Thus the equation (4) can be mathematically written as

Where is the laplacian operator. Thus in homogeneousregion where second term of both is zero, equation is zero becausegradient of the u and v are each determinedby laplace’s equation. Thus equation (1) can be now written as (5) (6)

Internal energy made up of first order terms which is and second order terms controlled controlled by . The first order term makes the Snake acts by like membrane and the second-order term makes it to zero at a point act like a thin plate. Setting allows snake to become second-order discontinuous and develop a corner.

When Snake will be at desired boundary at and will be zero because now there Snake is at boundary points so no further change is possible. So equation (5) and equation (6) can be written as (7) (8)

and are constants, When minimizingthe energy function gives the following two Euler equation.Thus by approximating the derivatives with finite differencesand converting to .The internal energy vector notation with can be written as

Thus the new set of points for Active contour model are (9) (10)

(3) Where h is the space between points in the contour .So the internal energy can be and written as pentadiagonal matrix A as shown in figure 3. 2) External Energy External energy force is defined by gradient vector flow(GVF) field. The GVF field points towards the object boundary and finally it gets towards image border. The main advantages of the GVF field are that it can capture snake from a long range from either side of the object boundary. It can be used into concave regions.

Figure 1(a) shows the input image (b) shows Gradient vector flow field of (a) and (c) shows Snake with Gradient vector force as external forces moves into the concave boundary region.

(4) Gradient Vector Flow(GVF) field can be defined as that the vector field minimizes the energy function. Thus in case of homogeneous region where there is no change in data , the energy is dominated by partial derivatives is large,the energy is of the vector field. When minimized by setting .

This model can be used to solve many image processing problems such as detection of edges, lines, contours and object tracking. By providing appropriate energy it is possible that to push the initial contour to the desired solution. Snake is used for semi-automatic image interpretation. So when there is no automatic starting mechanism exists, Active contour model can be used there.

The parameter µ is the regularization parameter governing the tradeoff between first term and the second term. This parameter should be set according to the amount of noise present in the image. If there

III. PROPOSED METHOD The block diagram of the proposed method is given in figure.



To localize contours, the idea is that we can identify a point of the contour on each active ray.Having the contour point in optimal value for the 2D image plane can easily be computed by (12) The ordering in the image plane is With given bythe angle i.e. we always know where the contour point n can be found, which corresponds to the direction . For this we only have to look from .Thus, no the reference point in direction crossings can occur in the contour. Active ray representation in Radial active ray is given in figure.

Figure 2 Block diagram of the proposed method.

The limination of Snake algorithm is that it is semiautomatic algorithm means it requires the selection of initial contour to move towards the desired contour and if this initial contour is too far from desired contour then it can not make desicion of whether to grow or shrink the initial contour. This problem is solved in the proposed method such that the initial contour for Snake algorithm is provided by output of radial active ray.

Figure 3 Representation of a contour point by active rays.

Using this we get the same representation of the contour as we get for active contour model. So this can be used as the initial contour for Active contour model. So that the problemof active contour is solved because contour we have afterapplying radial active ray will be much more closer to theactual contour so that it will be easier for the active contour model to get the desired contour.

A. Radial Active Ray Radial Active Ray can be used for Contour extraction. There is a difference between Active contour and Active ray. The main difference is that for active ray a unique ordering of contour elements in the 2D image plane is given, which cannot be found for active contours. This is advantageous for predicting the contour element’s position and prevents crossing in the contour. Second advantage of this approach is that localization of the contour points is reduced to 1D search problem on 1D signals compare to 2D image plane. These 1D signals are the gray values, which are sampled along a straight line from a reference point inside the contour in certain directions.

IV. EXPERIMENTAL RESULT The proposed method is tested on number of images and it gives good result compare to Snake with GVF alone.

For the representation, we define a reference point ,which has to lie within the image is contour. Then, a so called active ray as a 1D function defined on the image plane of the image, depending on those gray values which are on a straight line from the image point m in direction (11) Where

,

(a) (b) Figure 4(a) shows the input image and (b) shows the final result after applying Snake with GVF field.

is given by the image size.



(a) (b) (c) Figure 5(a) shows the input image with reference point,(b) shows the image after applying Radial active ray and (c) shows the final image after applying Radial active ray first and then Snake with GVF field.

V. CONCLUSION The proposed method for segmentation of deformable objects in image guided surgery uses Active contour model with GVF and Radial active ray. This Algorithm is tested on number of images. This algorithm is designed such that, First we have to select the reference point inside object region through mouse interface and then it gets initial contour using Radial active ray. After that it uses this initial contour as input to the Snake with GVF model. It effectively solve the limitation of Active contour model with GVF. The initial contour is provided by Radial active ray method which is faster compare to manual selection of initial contour. So the problem of Active contour model is be solved. The performance of this method can be further improved by using fuzzy clustering and with the knowledge of subjective contours. The speed of the implementation can be further improved but it will lead to less accuracy.

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